A general notion is unfolded to the mind by Exposition.
EXPOSITION. 1. The Nature of Exposition. ExPosmorr consists in such an analysis of a gen¬eral term as will make clear to the mind the general notion of which it is the sign. By "general term" is meant a word indicating a general notion. By "gen¬eral notion" is meant a mode of thought in which cer¬tain attributes are taken as belonging to certain objects, and as uniting them in one class. Thus "animal" includes the attributes "organized," "sentient," etc., and is applicable to such objects as "men," "horses," "dogs," etc., which make up the -class "animal" by possessing the attributes "organized," "sentient," etc., in common. A general term is distinguished from a singular term, such as Rome, Julius Ccesar, the Nile, indicating a single object. 2. Forms of Exposition. Exposition assumes two forms : (1) Exposition of the notion in itself ; and (2) exposition of the notion in its relation to other notions. In either of these forms of exposition, we may have single terms, or terms united in propositions. In order to avoid use¬less repetition, it may be stated that the exposition of the terms of a proposition is an exposition of the prop pm Ion itself. Thus in the proposition, "Free insti¬tutions are promotive of happiness," an exposition of the subject and the predicate would be an exposition of the whole proposition. The copula "are" requires no exposition. Any doubt with reference to the cop¬ula, is not a doubt as to the meaning, but as to the truth of the proposition. The truth of a proposition must be established by argument, which takes for granted the meaning of the terms, and is occupied with the negative or affirmative quality of the copula. Exposition elucidates the meaning of "free institu¬tions" and "promotive of happiness; and here its office ends. Argumentation then decides whether the copula should be "are" or "are—not." SECTION I. EXPOSITION OF THE NOTION IN ITSELF. 1. Comprehension and Extension. A general notion, or conception of a class, includes certain attributes and certain objects to which the at¬tributes belong. For example, the word man includes such attributes as rationality, intellectuality, voluntary power, etc., and also includes all the individual beings known to us as men. Man is also an animal, but this term includes a greater number of objects than the word man, for it embraces horses, dogs, etc. But these other animals do not possess rationality or intel¬lectuality. The class "animal" excludes common at¬tributes in proportion as it includes more objects. We have, then, in a general notion, two kinds of quantity : (1) cotnprehension, which is made up of the different attributes included in the notion ; and (2) ezlension which is made up of those objects which are included in the general notion. These two, comprehension and extension, are in an inverse ratio to each other. As we pass from "man" to "animal" the extension increases, but the comprehension diminishes ; the objects included are more numerous, the attributes implied are less nu¬merous. 2. Nature of a Definition. The exposition of the comprehension of a notion is its logical definition. Thus, in the notion man there are two constituent notions, the first including the at¬tributes of the notion animal, the second including the attributes of the notion rational. These constituent notions, animal and rational, may in turn be resolved in like manner into more elementary notions, and so on until those notions are so elementary as to satisfy the mind. In each of these processes of resolution we have one constituent notion which includes the notion de¬fined. This is called the genus. The other constitu¬ent notion distinguishes the notion defined from the genus, and is called the differentia. A definition is, therefore, a division of a general notion according to its attributes. It follows that a simple notion, which can be referred to no genus, cannot be defined. Thus being, the highest genus known to the mind, is inde¬finable. 3. Nature of Division.• The exposition of the extension of a notion is its division. Thus, the notion man includes under it white men, black men, red men, etc., divided according to color; Africans, Asiatics, Europeans, etc., divided according to geographical lines; Jews, Mohammedans, Buddhists, Christians, etc. divided according to religion. It is evident that the character of our division will de¬pend entirely upon the principle according to which we divide a notion into its constituent objects. It follows that a notion cannot be divided when it includes only one object. 4. Difference between Definition and Division. Definition and division are opposite processes. Comprehension is simply the sum of the qualities, characteristics or attributes of which a notion is com¬posed, and is resolved into its parts by definition. Ex¬tension is simply the sum or complement of the objects whose resembling characteristics constitute the general notion, and is resolved into its parts by division. De¬finition is a discrimination of attributes ; division a discrimination of objects. As the list of attributes is lengthened, the list of objects possessing them is shortened ; and vice versa. Being is the maximum of extension and the minimum of comprehension. In¬cluding the greatest number of objects, it includes the least number of attributes. 5. Kinds of Definition. Three principal kinds of definition are distinguished by Hamilton.. (1) Nominal.—Nominal definitions are mere ex. plications. They are, therefore, generally preliminary to a more precise distinction. Thus the nominal def¬inition of a circle is, "The word ' circle ' signifies a uniformly curved line." (2) Beals—In real definitions, the object defined is considered as existing, and the notion precedes the definition. They are merely analytic, nothing being given explicitly in the defining member which is not contained implicitly in the subject defined ; as, "A circle is a line returning upon itself, of which all the parts are equi-distant from a given point." (3) Gensta0.—The genetic definition represents the defined object as in the process of becoming. It is therefore synthetic ; as, "A circle is formed when we draw around, and always at the same distance from a fixed point, a movable point which leaves its trace, until the termination of the movement coincides with its commencement." The genetic definition is possible only when the objects to be defined are quantities rep¬resented in time or space. 6. The Laws of Logical Definition. The following are the laws of a strictly logical definition. (1) A definition must be adequate.—This neces sitates a genus and a differentia. A true definition will admit of .a transposition of the subject and the predicate. Such a transposition is an easy test of a definition. If "Man is a rational animal" be an ade¬quate definition, it must be true that a rational animal is a man ; for otherwise something besides men is in¬cluded in the definition. (2) A definition must not define by negative or divisive attributes.—We do not say what a notion is by saying what it is not ; nor do we define a notion by referring it to one class or another, which is a process of division. These expedients may properly precede and prepare the way for a definition, but they are not definitions. (8) A definition should not be tauthlogioal.—We cannot define an object by itself. This is called "de¬fining in a circle." This is a very common fault, and is fostered by the bilingual character of the English language, which renders it possible to define an Anglo- Saxon word by a Norman-French equivalent. The verbal form conceals the repetition of thought. This mode of explaining by equivalents is often useful, but must not be mistaken for a logical definition. (4) The definition must be mdse.—Any attribute not essential to the distinction only confuses it. The looseness of a definition leaves it open to refutation. The Platonic definition, "Man is a two-legged animal without feathers," was refuted by exhibiting a plucked bird, which, by transposition of the subject and predi¬cate, would be a man, if the definition were correct. (5) A definition should be perspiouous.—The very object of a definition is clearness. That it should itself be perspicuous is, therefore, self-evident. Brevity is generally necessary to perspicuity. Figurative language will often render definitions brilliant, but it will fre¬quently expose them to criticism for violaing this law. 7. Kinds of Divildon. (1) Partition.—The notion man may be regarded as made up of certain attributes ; as living being, ra¬tional, mortal, etc. This division of a notion into its component attributes is called partition. It differs from definition in enumerating all the attributes which make up a whole, while definition states only a genus and differentia. It differs from logical division in being a division of the comprehension, not of the extension. (2) Logloal Division.—A logical division is an ex¬position of the extension of a notion ; it enumerates, not the attributes but the species of a notion. Thus man may be divided into the various species together comprising the general notion man, and the division, as previously shown, may be according to any one of many principles. The principle of division is the one essential attribute according to which the division is made. The notion is called the divided whole ; its parts are the dividing members ; these with reference to one another are co-ordinates ; with reference to the divided whole, subordinates. 8. The Laws of Logical Division. The logical division of a notion is regulated by several laws. (1) Every Division should have some Principle. —The reason of this is manifest. If there be no attri¬bute with reference to which objects are classed, there can be no division. (2) Every Division should have but one Principle. —If there are two or more principles of division, there will be no division. Thus, to class men as white, Af¬rican, English, moral, and Jews, would not be a divis¬ion of men, for these classes include one another. (3) The Principle of Division should be an actual and essential character of the divided whole.—Unless such a principle be selected, there will be no distinct and recognizable line of demarcation between the sub¬ordinates. (4) No dividing member must of itself exhaust the extbject„ —This law follows from the axiom that a part is less than the whole. That then must be a faulty division which represents a part as exhausting the whole. A division of men into intelligent races and barbarous races, would violate this law, since all men possess some degree of intelligence, and are hence included under the first class. (6) The dividing members must together exhaust the notion, but not more,—Leaving out a distinct class violates this law. Thus, if we were to divide all actions into the morally good and the morally bad, excluding those which possess no moral quality, the division would be incorrect. This division would be a correct one of moral actions, but not of actions generally, since some are morally indifferent. If we wore to divide geometrical figures into surfaces, solids, lines, and points, we should more than exhaust the notion ex¬pressed by the word figures, for lines and points, though elements of figures, are not figures. (6) The dividing members should not include one another.—This law is often practically difficult to fol¬low. Presenting the same subordinate more than once is a violation of this law. A perfect exposition of a science would so classify its facts that they would ap¬pear but once. Practically this is almost impossible. Logic and Bsthetics, for example, are distinct from Rhetoric, but there could be no science of Rhetoric which should not repeat facts of Logic and /Esthetics. Again, the laws of Rhetoric are laws of mind, of idea, and of form, but they are all so interdependent that the same fact often reappears under each of these divisions. (7) A division should proceed continuously, without hiatus—Division may proceed through proximate or remote subdivisions. A perfect division does not leap over intermediate steps. Mathematicians may fot brevity say; "Angles are either right, or acute, or ob¬tuse." A continuous division would be, "Angles are either right or oblique ; and the oblique, either acute or obtuse." Imperfect. Cirofinuour. I. Right. 11. Right. Angles. S. Acute. / (1) Acute. A Obtuse 2. Oblique. (*Obtuse 9. Exposition of a Proposition A proposition may be explicated by the exposition of its terms. This exposition may be by definition or by division. The process may be illustrated. (1) By Deflnition.—A proposition may be expli¬cated by the definition of its terms. Let us take the proposition, "Democracy is promotive of liberty." Assuming that the word " promotive " needs no ex¬position, we have an exposition of this proposition when we have defined the terms " democracy " and "liberty." In seeking for the genus of "democracy," we must first decide whether we mean a form of gov¬ernment, a political party, or the avowed principles of that party. If we mean the first, form of government is the genus. The differentia is expressed in the phrase by the people, which distinguishes it from other forms of government. The logical definition of "de¬mocracy," in this sense, is, A form of government by the people. "Liberty" must now be defined. In its political sense, " liberty " may be referred to the genus state of society. It must now be distinguished from other states of society, such as license, anarchy or despotism. The differentia regulated by just laws distinguishes it from these, since license is lawless, anarchy is the absence of law, and despotism interferes with it. The definition of "liberty "is, A state of society regulated by just laws. Substituting the two definitions for the original terms, we have the proposition, A form of government by the people is promotive of a state of society regulated by just laws. This is an exposition by definition of the origi¬nal proposition. (2) By Division.—Let us take the proposition, "Free institutions are compatible with literary pro¬gress." Assuming that the expression "compatible with" needs no explanation, the exposition of the terms "free institutions" and "literary progress," is the ex¬position of the whole proposition. Before dividing the subject "free institutions," we must select a principle of division. Let it be the interests of society. These are educational, political, religious, commercial, indus¬trial, etc. We may then state the proposition thus : (educational. political, Free rceollgiTraal, institutions are compatible with literary progress. and industrial We may now divide the predicate. "Literary pro¬gress" may be divided into the progress of the differ¬ent departments embraced under the notion literature. These may be imperfectly enumerated as oratory, poetry, history, criticism, journalism. Substituting this complex predicate for the term "literary pro¬gress," we have this exposition of the original proposi. tion 1talacational,1 oratory, political, reetotili, Ins coreligiTAal, tinstitutions are compatible ,..4„,,,_, and 1 with are in '""`ag" industrial liournallam. It is important to note that if the expanded sub¬,feot and predicate agree, the truth of the original proposition is made evident. If, on the contrary, disagreement can be shown between any element of the expanded predicate and any element of the expanded subject, it shows that the original proposition is not universally true. SECTION IL EXPOSITION OF THE NOTION THROUGH ITS RELATIONS. When the logical exposition of a notion is not con¬venient, it may be explicated through its relation to other notions. Several methods of doing this may be enumerated. 1. The Method of Particulars. We may explicate a notion by mentioning particu¬lar cases or concrete instances. This is a simple expe¬dient, adapted to a low order of intelligence, and re¬quiring no powers of generalization. Thus, poetry may be explained by enumerating representative poems, and beauty by concrete examples of the beautiful in objects. 2. The .Method of Conditions. A second method of explicating a notion is to men¬tion the conditions essential to its production or exis¬ tence. Thus the notion dew may be explained by the enumeration of the circumstances in which the moist¬ure of atmospheric vapor condenses. Cause and effect are both included under this head. 3. The Method of Sinillars. A general notion may be explained by comparing it to similar notions. No direct similitude is necessary, , but simply a resemblance of relations. Our notions of divinity and supernatural beings are explicated through our notions of being and spirit as they are known to us in consciousness. Hence many of the most impor¬tant ideas of philosophy and religion are explicated in this way. 4. The Method of Contrast. We may give an exposition of a notion through its opposite. All knowledge is double. Heat and cold, light and darkness, good and evil, are fixed in thought as opposite poles. Some of our most common notions can be discriminated only by this method. The no¬tion of self, or the Ego, is distinguished from the not self, or non-Ego, by the method of contrast.